The second order optimality conditions for nonlinear mathematical programming with C 1,1 data

Abstract

To find nonlinear minimization problems are considered and standard C2-regularity assumptions on the criterion function and constrained functions are reduced to C1,1-regularity. With the aid of the generalized second order directional derivative for C1,1 real-valued functions, a new second order necessary optimality condition and a new second order sufficient optimality condition for these problems are derived.